The sum of two angles is $87^\circ$. Angle 2 is $45^\circ$ smaller than $2$ times angle 1. What are the measures of the two angles in degrees?
Solution: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 87}$ ${y = 2x-45}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${2x-45}$ for $y$ in the first equation. ${x + }{(2x-45)}{= 87}$ Simplify and solve for $x$ $ x+2x - 45 = 87 $ $ 3x-45 = 87 $ $ 3x = 132 $ $ x = \dfrac{132}{3} $ ${x = 44}$ Now that you know ${x = 44}$ , plug it back into $ {y = 2x-45}$ to find $y$ ${y = 2}{(44)}{ - 45}$ $y = 88 - 45$ ${y = 43}$ You can also plug ${x = 44}$ into $ {x+y = 87}$ and get the same answer for $y$ ${(44)}{ + y = 87}$ ${y = 43}$ The measure of angle 1 is $44^\circ$ and the measure of angle 2 is $43^\circ$.